摘要
通过下列步骤,构造了一维Tonks-Girardeau原子气区域中Gross-Pitaevskii方程的新解.步骤一,通过函数变换,把一维Tonks-Girardeau原子气区域中Gross-Pitaevskii方程的求解问题转化为一种非线性常微分方程的求解问题.步骤二,给出了一种非线性常微分方程与第二种椭圆方程的拟Bcklund变换.步骤三,利用第二种椭圆方程的新解和Bcklund变换,构造了一维Tonks-Girardeau原子气区域中Gross-Pitaevskii方程的无穷序列新解.
The following steps are given to search for new solutions of Gross-Pitaevskii equation in a one-dimensional Tonks-Girardeau atomic gas field. Step one, according to a function transforma- tion, the solving of Gross-Pitaevskii equation in a one-dimensional Tonks-Girardeau atomic gas field is changed into the solving of a kind of nonlinear ordinary differential equations. Step two,a kind of nonlinear ordinary differential equations and the quasi-B^icklund transformation of the second kind of elliptic equations are obtained. Finally, new infinite sequence solutions of Gross-Pitaevskii equa- tion in one-dimensional Tonks-Girardeau atomic gas fields are constructed by applying new solu- tions and Backlund transformation of the second kind of elliptic equations.
出处
《内蒙古大学学报（自然科学版）》
CAS
北大核心
2015年第6期574-581,共8页
Journal of Inner Mongolia University：Natural Science Edition
基金
国家自然科学基金资助项目(11361040)
内蒙古自治区高等学校科学研究基金资助(NJZY12031)
内蒙古自治区自然科学基金资助(2015MS0128)
